Partial restoration of the wave spectrum of a superlattice due to cross correlations between one- and three-dimensional inhomogeneities

Effects of cross correlations between one-dimensional (1D) and three-dimensional (3D) random inhomogeneities on the wave spectrum in sinusoidal superlattices are studied theoretically. The situation when the gap in the spectrum (the forbidden zone) at the first Brillouin zone boundary of the superlattice is closed under the action of the 1D inhomogeneities is considered. The phenomenon of the partial opening of this gap is found when the 3D inhomogeneities cross correlated with the 1D inhomogeneities add to the superlattice. The appearance of the logarithmic resonance in the center of the forbidden zone under the action of the cross correlations is shown. The physical nature of the effects in the wave spectrum of the superlattice that are caused by the cross correlations and the relation of these effects with the asymptotic properties of the correlation function of inhomogeneities are discussed.